4 beads and 1 marble cost $20.30.
1 bead and 4 marbles cost $15.20.
- Find the cost of 1 bead and 1 marble.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
- Find the cost of 7 beads and 7 marbles.
(a)
4 beads + 1 marble = 20.30 --- (1)
1 bead + 4 marbles = 15.20 --- (2)
(1) + (2)
5 beads + 5 marbles = 20.30 + 15.20
5 beads + 5 marbles = 35.50 --- (3)
(3)
÷ 55 beads + 5 marbles = 35.50
1 bead + 1 marble = 35.50 ÷ 5
1 bead + 1 marble = 7.10 --- (4)
(b)
(2) - (4)
(1 bead + 4 marbles) - (1 bead + 1 marble) = 15.20 - 7.10
1 bead - 1 bead + 4 marbles - 1 marble = 8.10
3 marbles = 8.10
1 marble = 8.10 ÷ 3 = 2.70
Cost of 1 marble = $2.70
(c)
Substitute 1 marble = 2.70 into (4).
1 bead + 1 marble = 7.10
1 bead + 2.70 = 7.10
1 bead = 7.10 - 2.70 = 4.40
Cost of 1 bead = $4.40
(d)
(4)
x 7 1 bead + 1 marble = 7.10
7 x (1 bead + 1 marble) = 7 x 7.10
7 beads + 7 marbles = 49.70
Cost of 7 beads and 7 marbles = $49.70
Answer(s): (a) $7.10; (b) $2.70; (c) $4.40; (d) $49.70